7. Superposition Theorem - Components
The superposition theorem extends the use of Ohm’s Law to
circuits with multiple voltage or current sources.
In order to apply the superposition, all the components must be
linear, or “Ohmic”, meaning that the component obeys Ohm’s
Law
Yes: Resistors, Capacitors, Inductors
No: Transistors, semiconductor diodes, and electron tubes,
Operational Amplifiers. Such components are never bilateral
and seldom linear.
8. Superposition Theorem
The Superposition is useful when we have more than one
Voltage Source or more than one Current Source
We will only consider Voltage Sources in this course
9. This analysis is done by calculating the current contributed by
each source, and then adding or subtracting (i.e. taking the
Superposition) the currents contributed by each source
10. 7-2: Current Dividers with
Two Parallel Resistances
This slide applies to the special case where we have just 2
resistors in parallel
IT is divided into individual branch currents.
Each branch current is inversely proportional to the branch
resistance value.
For two (and only 2) resistors, R1 and R2, in parallel:
13. 5
Determine The Currents going through each resistors
Last time, we analyzed this circuit and determined the total
current was 2 Amps. All of the current flows through R1 and
R2, so the current in those resistors must be 2 Amps
2A
2A
14. Determine The Currents going through each resistors
At Point A, the current splits into two branches. The resistance
of Branch 1 is R5 = 10Ω. Last time, we determined the
resistance of branch 2 was also 10Ω
2A
2A
15. Determine The Currents going through each resistors
2 Amps enters node A. We can use the current divider to
determine the current leaving node A.
2A
16.
17. 8
Determine The Currents going through each resistors
Since 1 Amp goes into each branch, we know the currents
through R5 and R6 are each 1 Amp. Use the current divider to
find the current through the 12 Ohm resistors.
2A
2A
1A
1A
0.5A
0.5A
1A
26. R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3
Now that we know the total current is 0.141A, we can apply the
current divider approach to find the current through Resistors 1
and 2
27. 12
Step 1 - Direction of Current through R3
The total current leaves V1 from the positive (top) terminal and
passes through R1. It then splits into two branches. The
current passing through R3 is going in in the downward
direction.
R1
R2
33. Step 2 – Find RT and IT
Step 2: Short Voltage Source V1. Find I3
34. 15
Step 2 – Find R3
Step 2: Short Voltage Source V1. Find I3
35. 16
Step 2 - Direction of Current through R3
The total current leaves V2 from the positive (top) terminal and
passes through R2. It then splits into two branches. The
current passing through R3 is going in in the downward
direction.
Step 1: Short Voltage Source V2. Find I3
37. smaller from the larger. The direction of the current is the same
as the direction of the larger current.
Case 2: Currents are going in the same direction: Add the
currents. The resulting current is in the same direction as both
currents.
Step 3 Add or Subtract the Currents to Determine R3 for the
Original Circuit
39. Lab #3 Worksheet
Watch the Video on eCampus. For each of the Series-Parallel
circuits:
1) Build the circuit in Multisim Live and “measure” the Total
Current and the current in each of the
parallel branches.
2) Calculate the Total Resistance, RT, of the Circuit.
3) Using RT, use Ohm's Law to calculate the total current, IT.
4) Use IT current divider formula to determine the current in
each of the resistors. Draw the
40. direction of each current on the diagram.
Scan and upload your work in eCampus. If you do not have a
scanner, use a scanning phone app such as
Google Drive, Office Lens, or Camscanner.
Current Divider: �� = �� (
��
��+��
)
1. Find the current magnitude and direction in each resistor
using the current divider formula.
(Remember: The current is the same for resistors that are in
series with each other.)
2. Find the current magnitude and direction in each resistor
using the current divider formula. Hint:
First find the current through R2. The current will first branch
at node A. The first branch has
resistance R2. The 2nd branch resistance will be the combined
resistance of resistors 4-9. Trace a
path from point A to point B to determine which of theses
resistors are in series and which are in
parallel and calculate accordingly.
41. https://www.youtube.com/watch?v=-
fQrjiIbI_s&feature=youtu.be&ab_channel=KoryGoldammer
Upload your Lab 3 Deliverables here. A formal lab report
is not required for this lab.
1) File containing your Multisim screen shots (please paste all
of your screen shots into a single file).
2) The lab document with your answers filled in (handwriting
is fine).
3) A scan of your calculations using the formulas used to
obtain your answers.
If you do not have access to a scanner, please use a
scanning app, such as Google Drive, Office Lens, or
Camscanner.
1
ENGR2105 Lab3 Superposition Theorem
Student Name __________________________________
Objectives:
To solve a network containing resistors and multiple power
sources. To learn the use of a
computer to solve electrical circuits and compare calculated
results with simulated results.
42. Materials:
Computer to access Multisim Live. Calculator.
Background Information:
The Superposition Theorem can be used to solve circuits
including resistors and multiple
sources. It can be applied only when all the components are
linear and passive. The main idea is
that the effect of all power sources can be found by summing
the effects of each power source
individually.
You are expected to show all the formulas and calculations
needed to find the answers. These
can be handwritten in the worksheets. Take screenshots of each
of the Multisim measurements
that you take.
2
ENGR2105 Lab3 Superposition Theorem Worksheet
43. Apply Superposition Theorem to Circuit 1 to find the current
through Resistor 2:
Fig 1. Circuit1
Procedure:
• Build the circuit in Fig1 in MultiSim.
• Measure the voltage potential at point Pcurrent through each
resistor (Screen Shot):
Measured I_2 = ________________
• Apply Superposition Theorem to the circuit in Fig 1.
Step1: Short power supply V2
Step2: Calculate the current through R2 for this circuit. This is
the contribution to the
current from power supply V1.
Step3: Build this circuit in MultiSim and verify the current
through R2. (Screen Shot)
Calculated I_2 = ________ Measured I_2 =________ Direction
= ____________
Step4: Reconnect the Power Supply V2 and short power supply
V1.
Step 5: Calculate the current through R2 for this circuit. This is
44. the contribution to the
current from power supply V2. Build this circuit in Multisim
and measure the
current. (Screen Shot)
Calculated I_2 = ________ Measured I_2 =________ Direction
= ____________
Step6: Combine the effects of the two power supplies by adding
or subtracting the two
currents (Hint: Are the power supplies pushing positive charge
in the same
direction?.
Calculated I_2 = ________________ Direction of I_2 =
________________
Does it match what you found in the first measurement? If not,
something is wrong.
3
Apply Superposition Theorem to Circuit 2 to find the current
through R3.
Fig 2. Circuit2
Procedure:
45. • Build the circuit in Fig. 2 in MultiSim. Pay attention to the
polarity (orientation) of V2
throughout this problem.
• Use Multisim to measure the current through R3 (Screen
Shot):
Measured I_3 = ________________
• Apply Superposition Theorem to the circuit in Fig 2.
Step1: Short power supply V2
Step2: Calculate the current through R3. This is the contribution
from power supply V1.
Step3: Build this circuit in Multisim and measure R3 to verify
your result. (Screen
Shot)
Calculated I_3 = ________ Measured I_3 =________ Direction
= ____________
Step4: Restore V2 and short V1. Pay attention to the polarity
(orientation) of V2!
Compute the current through R3. This is the contribution from
power supply V2.
Step5: Build the circuit in Fig 2 in MultiSim and measure the
current through R3
46. (Screen Shot).
Calculated I_3 = ________ Measured I_3 =________ Direction
= ____________
Step6: Add the effects of the two power supplies by adding OR
subtracting the two
currents
Calculated I_3 = ________________ Direction =
____________
Does it match what you found in the first measurement? If not,
something went wrong.
